= Feynman-Kitaev Hamiltonian
{c}
{title2=$H_{\rm in}+H_{\rm prop}+H_{\rm out}$}
= Kitaev circuit Hamiltonian
{c}
{synonym}
A <Feynman-Kitaev Hamiltonian> penalizes incorrect input initialization, disagreement between successive <quantum circuit> steps and clock labels, and optionally a rejecting output. Its propagation <quadratic form> is a sum of $\tfrac12\|\eta_t-U_t\eta_{t-1}\|^2$. Without output penalty, its zero-energy space consists of correctly initialized <computational history states>. A <nonlocal quantum clock> makes the propagation formula simple but does not supply fixed qubit locality by itself.
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